Finite Group Databasebeta

← #44534968

Subgroups — #44534968

Order 31347.

950 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 950 conjugacy classes of subgroups — too many to draw. Only its 280 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C32⋊(C43⋊C3)C311yesmaximal, characteristic
2#23782805C313yesmaximal, complemented
3#23782804C313yesmaximal, complemented
4#23782801C319yesmaximal, complemented
5#23782799C319yesmaximal, complemented
6#23782798C311yesmaximal, characteristic, complemented
7#23782797C313yesmaximal, complemented
8#23782796C313yesmaximal, complemented
9#23782783C313yesmaximal, complemented
10C3×C32⋊(C43⋊C9)C311yesmaximal, characteristic, complemented
11C32⋊C9×C43⋊C3C313yesmaximal, complemented
12C43×#6891C311yesmaximal, characteristic, complemented
13C33×C43⋊C3C3213yes—
14C3×#11923958C3213yescomplemented
15C3×#11923957C3219yescomplemented
16C3×#11923956C3219yescomplemented
17C3×C32⋊(C43⋊C3)—39no—
18C3×C32⋊(C43⋊C3)C3213yes—
19C3×C32⋊(C43⋊C3)C3213yes—
20C3×C32⋊(C43⋊C3)C3211yescharacteristic
21C3×C32⋊(C43⋊C3)C3211yescharacteristic
22C3×C32⋊(C43⋊C3)C3211yescharacteristic
23C32×C43⋊C9C3213yescomplemented
24C3×C9×C43⋊C3C3219yescomplemented
25C32⋊(C43⋊C9)C3211yescharacteristic
26C32⋊(C43⋊C9)C3213yes—
27C32⋊(C43⋊C9)C3211yescharacteristic
28C32⋊(C43⋊C9)C3211yescharacteristic
29C32⋊(C43⋊C9)C3213yescomplemented
30C32⋊(C43⋊C9)C3213yescomplemented
31C32⋊(C43⋊C9)C3213yescomplemented
32C32⋊(C43⋊C9)C3213yescomplemented
33(C3×C43⋊C3)⋊C9C3219yescomplemented
34(C3×C43⋊C3)⋊C9C3219yescomplemented
35(C3×C43⋊C3)⋊C9C3219yescomplemented
36(C3×C43⋊C3)⋊C9C3219yescomplemented
37(C3×C43⋊C3)⋊C9C3219yescomplemented
38(C3×C43⋊C3)⋊C9C3219yescomplemented
39C34×C43C3211yescharacteristic
40C3×3−1+2×C43C3213yescomplemented
41C43×C32⋊C9C3213yes—
42C43×C32⋊C9C3213yescomplemented
43C43×C32⋊C9C3213yescomplemented
44C32×C43⋊C3—39no—
45C32×C43⋊C3—39no—
46C32×C43⋊C3—93no—
47C32×C43⋊C3—93no—
48C32×C43⋊C3C3313yes—
49C32×C43⋊C3C3313yes—
50C32×C43⋊C3C3313yes—
51#11923958—93no—
52#11923957—99no—
53#11923956—99no—
54C32⋊(C43⋊C3)—33no—
55C32⋊(C43⋊C3)—33no—
56C32⋊(C43⋊C3)—39no—
57C32⋊(C43⋊C3)—39no—
58C32⋊(C43⋊C3)3−1+219yescomplemented
59C3×C43⋊C9—93no—
60C3×C43⋊C9C3313yes—
61C3×C43⋊C9C3319yes—
62C3×C43⋊C9C3313yes—
63C3×C43⋊C9C3313yes—
64C9×C43⋊C3—99no—
65C33×C43—33no—
66C33×C43—33no—
67C33×C43—91no—
68C33×C43—91no—
69C33×C43C3311yescharacteristic
70C33×C43C3311yescharacteristic
71C33×C43C3311yescharacteristic
72C33×C43C3311yescharacteristic
733−1+2×C43—93no—
74C3×C9×C43C3319yes—
75#10624897—431nomaximal, Sylow
76C32×C43—31no—
77C32×C43—31no—
78C32×C43—31no—
79C32×C43—31no—
80C32×C43—31no—
81C32×C43—31no—
82C32×C43—31no—
83C32×C43—31no—
84C32×C43—31no—
85C32×C43—31no—
86C32×C43—31no—
87C32×C43—31no—
88C32×C43—31no—
89C32×C43—31no—
90C32×C43—99no—
91C32×C43C3×3−1+213yes—
92C32×C43#73713yes—
93C32×C43C3411yescharacteristic
94C3×C43⋊C3—33no—
95C3×C43⋊C3—33no—
96C3×C43⋊C3—33no—
97C3×C43⋊C3—33no—
98C3×C43⋊C3—33no—
99C3×C43⋊C3—33no—
100C3×C43⋊C3—33no—
101C3×C43⋊C3—33no—
102C3×C43⋊C3—33no—
103C3×C43⋊C3—33no—
104C3×C43⋊C3—33no—
105C3×C43⋊C3—927no—
106C3×C43⋊C3C3×3−1+219yes—
107C9×C43—39no—
108C43⋊C9—33no—
109C43⋊C9—39no—
110C43⋊C9—33no—
111C43⋊C9—33no—
112C32×H(3,𝔽3)—431no—
113C9⋊H(3,𝔽3)—439no—
114C9⋊H(3,𝔽3)—439no—
115C9⋊H(3,𝔽3)—433no—
116C9⋊H(3,𝔽3)—433no—
117#6891—431no—
118#6891—433no—
119#6891—433no—
120#6891C43⋊C311yescharacteristic, complemented
121C9×H(3,𝔽3)—433no—
122C3×C32⋊C9—431no—
123C3×C32⋊C9—433no—
124C3×C43—33no—
125C3×C43—33no—
126C3×C43—91no—
127C3×C43—91no—
128C3×C43C32×3−1+211yescharacteristic
129C3×C43C3×#73711yescharacteristic
130C3×C43H(5,𝔽3)11yescharacteristic
131C3×C433−1+411yescharacteristic
132C43⋊C3—39no—
133C43⋊C3—93no—
134C43⋊C3—93no—
135C34—433no—
136C34C3×C43⋊C311yescharacteristic
137C3×3−1+2—433no—
138C3×3−1+2—439no—
139C3×3−1+2—439no—
140C3×3−1+2C3×C43⋊C313yescomplemented
141C3×H(3,𝔽3)—431no—
142C3×H(3,𝔽3)—433no—
143C3×H(3,𝔽3)—433no—
144C3×H(3,𝔽3)—431no—
145C3×H(3,𝔽3)—431no—
146C3×H(3,𝔽3)—1299no—
147C32×C9—433no—
148C32×C9—439no—
149C32⋊C9—431no—
150C32⋊C9—433no—
151C32⋊C9—431no—
152C32⋊C9—431no—
153C32⋊C9—433no—
154C32⋊C9—433no—
155C32⋊C9—433no—
156C32⋊C9—433no—
157C32⋊C9—439no—
158C32⋊C9—439no—
159C32⋊C9—439no—
160C32⋊C9—439no—
161C32⋊C9—439no—
162C32⋊C9—439no—
163C32⋊C9C3×C43⋊C313yes—
164C32⋊C9C3×C43⋊C313yescomplemented
165C32⋊C9C3×C43⋊C313yescomplemented
166C43#1062489711yescharacteristic, complemented, Sylow
167C33—33no—
168C33—33no—
169C33—91no—
170C33—91no—
171C33—433no—
172C33—433no—
173C33—433no—
174C33—1299no—
175C33—1299no—
176C33—3873no—
177C33—3873no—
178C33C32×C43⋊C311yescharacteristic
179C33C32×C43⋊C311yescharacteristic
180C33C32×C43⋊C311yescharacteristic
181C33C32×C43⋊C311yescharacteristic
1823−1+2—93no—
1833−1+2—3879no—
1843−1+2—3879no—
1853−1+2—3873no—
186H(3,𝔽3)—439no—
187H(3,𝔽3)—1299no—
188H(3,𝔽3)—1299no—
189H(3,𝔽3)—1293no—
190H(3,𝔽3)—1293no—
191C3×C9—433no—
192C3×C9—433no—
193C3×C9—433no—
194C3×C9—439no—
195C3×C9—3879no—
196C3×C9—3873no—
197C3×C9C32×C43⋊C319yes—
198C32—31no—
199C32—31no—
200C32—31no—
201C32—31no—
202C32—31no—
203C32—31no—
204C32—31no—
205C32—31no—
206C32—31no—
207C32—31no—
208C32—31no—
209C32—31no—
210C32—31no—
211C32—31no—
212C32—99no—
213C32—439no—
214C32—1293no—
215C32—1293no—
216C32—1293no—
217C32—1293no—
218C32—1293no—
219C32—1293no—
220C32—1293no—
221C32—1293no—
222C32—1293no—
223C32—1293no—
224C32—1293no—
225C32—38727no—
226C323−1+2×C43⋊C313yes—
227C32#1681252613yes—
228C32C33×C43⋊C311yescharacteristic
229C9—39no—
230C9—1293no—
231C9—1299no—
232C9—1293no—
233C9—1293no—
234C3—33no—
235C3—33no—
236C3—91no—
237C3—91no—
238C3—1299no—
239C3—3873no—
240C3—3873no—
241C3C3×3−1+2×C43⋊C311yescharacteristic
242C3C3×#1681252611yescharacteristic
243C3C43⋊H(5,𝔽3)11yescharacteristic
244C3#2378292311yescharacteristic
subgroupG/H
center, FrattiniC32C33×C43⋊C3
commutator, socle, cosocleC32×C43C34
FittingC43×#6891C3
prime radicalC32×C32⋊(C43⋊C3)C3
hypercenter#6891C43⋊C3
hypocenterC43#10624897
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C32 ◁ #6891

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #23782805C3semidirect
3. #23782804C3semidirect
4. #23782801C3semidirect
5. #23782799C3semidirect
6. #23782798C3semidirect
7. #23782797C3semidirect
8. #23782796C3semidirect
9. #23782783C3semidirect
10. C3×C32⋊(C43⋊C9)C3semidirect
11. C32⋊C9×C43⋊C3C3semidirect
12. C43×#6891C3semidirect
14. C3×#11923958C32semidirect
15. C3×#11923957C32semidirect
16. C3×#11923956C32semidirect
23. C32×C43⋊C9C32semidirect
24. C3×C9×C43⋊C3C32semidirect
29. C32⋊(C43⋊C9)C32semidirect
30. C32⋊(C43⋊C9)C32semidirect
31. C32⋊(C43⋊C9)C32semidirect
32. C32⋊(C43⋊C9)C32semidirect
33. (C3×C43⋊C3)⋊C9C32semidirect
34. (C3×C43⋊C3)⋊C9C32semidirect
35. (C3×C43⋊C3)⋊C9C32semidirect
36. (C3×C43⋊C3)⋊C9C32semidirect
37. (C3×C43⋊C3)⋊C9C32semidirect
38. (C3×C43⋊C3)⋊C9C32semidirect
40. C3×3−1+2×C43C32semidirect
42. C43×C32⋊C9C32semidirect
43. C43×C32⋊C9C32semidirect
58. C32⋊(C43⋊C3)3−1+2semidirect
120. #6891C43⋊C3semidirect
140. C3×3−1+2C3×C43⋊C3semidirect
164. C32⋊C9C3×C43⋊C3semidirect
165. C32⋊C9C3×C43⋊C3semidirect
166. C43#10624897semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×C32⋊(C43⋊C3)3
#237828053
#237828043
#237828013
#237827993
#237827983
#237827973
#237827963
#237827833
C3×C32⋊(C43⋊C9)3
C32⋊C9×C43⋊C33
C43×#68913
#1062489743